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st: Why include leads (in a model with lags)?


From   Misha Spisok <misha.spisok@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Why include leads (in a model with lags)?
Date   Wed, 30 Sep 2009 17:44:50 -0700

Hello, Statalist!

My question in brief is, "What does including leads in a model that
'should' only have lags tell me?"

My intuition is that if leads are statistically signficant, then
something funky is going on (e.g., "How could future crime rates
'predict' current law enforcement expenditures?", or "How could future
unemployment rates 'predict' current GDP growth?").  However,
"something funky" is not intellectually satisfying.

I am considering a model of the following form:

y_t = b_0 + b_1*X_t + b_2*X_t-1 + b_3*X_t-2 + u_t

It was suggested to me to use lead values of X, e.g., estimating a
model of the form,

y_t = b_0 + b_1*X_t + b_2*X_t-1 + b_3*X_t-2 + b_4*X_t+1 + b_5*X_t+2 + e_t

If the coefficients b_4 or b_5 are statistically different from zero,
should this be cause for alarm?  If so, why?

Is there a command in Stata (or other references, a tutorial, etc.)
that can help me understand this (possible) problem better?

Best,

Misha
Using Stata 10.1
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